Continued from https://www.lesswrong.com/posts/NvNmDWEpr8FSicgYN/reasons-for-punishment

In the previous post we listed a number of reasons given for punishing people. The first was as preventation.

In some cases punishment can prevent the person being able to commit the crime in the future. For example it's much more difficult to commit certain crimes in prison. This is relevant if you believe people who commit such crimes once are more likely to do it again.

In this post I would like to analyze this from a game theoretic perspective.

Preventative Policies

There are actions that we do not want people to do (crimes), and there are policies we can take to reduce the chance of anyone being able to commit those crimes.

For example we don't want people to murder other people. In order to reduce the chance of murder, we could ban guns, and we could also ban all sharp implements.

However such policies have costs. If you ban guns people will find protecting themselves from bears harder. If you ban sharp implements people will find cooking a real challenge.

So in order to weigh up whether or not to impose some policy to reduce a crime, we have to consider (possible units in brackets):

1. The prior likelihood of the crime (average cases per person per year). 
2. The damage caused by the crime if it occurs (per instance).
3. The amount the policy will reduce the likelihood of the crime (average cases per person per year).
4. The cost of the policy (per person per year).

If (cost of the policy) < (reduction in likelihood of crime) * (damage caused by crime) then the policy is worth implementing.

For a given crime different policies will come out differently from this calculation. Hence why some countries ban guns, but none that I know of ban sharp implements.

This assumes we can only apply the policy on a blanket level. But these factors are different for every individual. Some people are more likely to commit crimes, some people will suffer more from the policy, and so on.

Hence why every country which bans guns allows soldiers to have them - the cost of banning guns is much higher for soldiers. And many polities ban children from having sharp implements - the chance of them hurting someone with them is much higher.

By applying a customized policy to each individual you can get better total utility than you can by having a single policy that applies to all people. The cost of this is complexity, which makes designing and implementing individual policies harder, and enforcement more difficult.

In practice we usually apply a compromise, dividing up the population into a few broad, easily distinguishable categories, with a single policy for each category. We may divide things up based on age, profession, health etc. Dividing up the population based on a category which doesn't seem all that relevant can be a sign of prejudice - e.g race or gender.

Punishment and Preventation

As we gain more information about a person, we may update which policy to apply to them. For example, in countries where guns are banned, if you can prove that you are have a safe temperament, and have a need for a gun, you can get a gun licence, and you can lose that gun licence if evidence is found that you hang out on extremist sites.

If someone commits a crime, that provides us with information that he is likely to commit the crime in the future. As such some policies which previously wouldn't have been worth it now become worth it. For example, very few people commit murder, but those that do are reasonably likely to commit murder again in the future. Locking someone up for the majority of their life so they can't murder anyone is clearly an extremely excessive policy for someone who has a 0.1% chance of killing someone, but not so obviously excessive for someone with a 50% chance.

Therefore when someone commits a crime we may impose a policy on them with a very heavy cost, if the updated likelihood of them committing a crime is high enough to justify it.

From this perspective this isn't really a punishment. We would act exactly the same way whether or not the crime was intentional or completely accidental, assuming that doesn't affect the likelihood of it happening again. We would also act exactly the same way whether or not they actually committed the crime, or we found out through some other means that they were likely to commit the crime in the future. If we had an oracle which would tell us how likely a given person is to commit a certain crime, we would never update based on crimes they actually committed, and so we would never have different policies for criminals and non-criminals.

There are two ways in this gets slightly more involved. Firstly criminals is a broad, well defined category, without many people prepared to speak up for them if they are prejudiced against, and who already have records in the legal system. Hence they make an ideal category for applying different policies to than the rest of the population (and so there's a reason to differentiate actual criminals from would be criminals).

Secondly once you have decided to to apply specific policies to criminals, then the act of committing the crime signals that the cost of such policies is relatively low to the criminal (or they wouldn't have committed the crime), so it may be worth applying an even stricter policy. This would tend to make the policies you would apply to criminal stricter than those where individuals don't opt in to being in a special cased category (and hence there's a reason to differentiate intentional criminals from unintentional ones).

Punishment as Preventation in Practice

For this series I'm particularly interested in prison. So to what extent do current justice systems send people to prison as a preventative from them committing crimes?

I'm no expert at all on the legal system, but my guess is that this doesn't really drive much.

Firstly, according to my contact in British legal system, from an official policy perspective there's no provision for sending someone to prison to 'keep them off the streets'. Whilst this may play into judges thinking, it does so purely at an unofficial level - prison is about what you did, not what you might do.

Secondly, most prison sentences are relatively short. Why would we assume that someone who commits a crime today is likely to do so again tomorrow, but not in two years? If the aim of prisons was to prevent the criminal acting again, you would expect most prison sentences to be for life - or at least till they're too old to commit the crime.

Thirdly, court cases tend to revolve almost entirely around what the person under trial did, and how morally culpable he was, not around what he's likely to do in the future.

So whilst preventation might be a small part of the motivation for prison sentences, they definitely are not the main motivation.